Colloquium Publications
Volume: 20;
1935;
405 pp;
Softcover
MSC: Primary 30;
Print ISBN: 978-0-8218-1020-0
Product Code: COLL/20
List Price: $79.00
AMS Member Price: $63.20
MAA Member Price: $71.10
Electronic ISBN: 978-1-4704-3168-6
Product Code: COLL/20.E
List Price: $79.00
AMS Member Price: $63.20
MAA Member Price: $71.10
Interpolation and Approximation by Rational Functions in the Complex Domain
Share this pageJ. L. Walsh
The present work is restricted to the representation of functions in the complex domain, particularly analytic functions, by sequences of polynomials or of more general rational functions whose poles are preassigned, the sequences being defined either by interpolation or by extremal properties (i.e. best approximation). Taylor's series plays a central role in this entire study, for it has properties of both interpolation and best approximation, and serves as a guide throughout the whole treatise. Indeed, almost every result given on the representation of functions is concerned with a generalization either of Taylor's series or of some property of Taylor's series—the title “Generalizations of Taylor's Series” would be appropriate.
Table of Contents
Table of Contents
Interpolation and Approximation by Rational Functions in the Complex Domain
- Cover Cover11
- Title page i2
- Preface iii4
- Preface to Second Edition vi7
- Contents vii8
- Chapter I. Possibility of approximation, analytic functions 112
- Chapter II. Possibility of approximation, continued 2738
- Chapter III. Interpolation and lemniscates 4960
- Chapter IV. Degree of convergence of polynomials. Overconvergence 6576
- Chapter V. Best Approximation by polynomials 89100
- Chapter VI. Orthogonality and least squares 111122
- Chapter VII. Interpolation by polynomials 152163
- Chapter VIII. Interpolation by rational functions 184195
- Chapter IX. Approximation by rational functions 224235
- Chapter X. Interpolation and functions analytic in the unit circle 281292
- Chapter XI. Approximation with auxiliary conditions and to non-analytic functions 310321
- Chapter XII. Existence and uniqueness of rational functions of best approximation 348359
- Appendix 367378
- Bibliography 383394
- Index 397408
- Back Cover Back Cover1417